Problem: Simplify; express your answer in exponential form. Assume $q\neq 0, n\neq 0$. $\dfrac{{q^{-4}}}{{(q^{4}n^{-1})^{-5}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${q^{-4} = q^{-4}}$ In the denominator, we can use the distributive property of exponents. ${(q^{4}n^{-1})^{-5} = (q^{4})^{-5}(n^{-1})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{q^{-4}}}{{(q^{4}n^{-1})^{-5}}} = \dfrac{{q^{-4}}}{{q^{-20}n^{5}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-4}}}{{q^{-20}n^{5}}} = \dfrac{{q^{-4}}}{{q^{-20}}} \cdot \dfrac{{1}}{{n^{5}}} = q^{{-4} - {(-20)}} \cdot n^{- {5}} = q^{16}n^{-5}$.